### Abstract

Cohen, Friedland, Kato, and Kelly conjectured that F(t)≡log r(e^{At}e^{Bt}) is convex for real t when A is nonnegative and B is diagonal; here r is the spectral radius. While the conjecture is correct for dimension n=1 or 2, it is shown here to be false for n≥3. Similarly t → logTrace(e^{At}e^{Bt})k need not be convex when n≥3.

Original language | English (US) |
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Pages (from-to) | 271-273 |

Number of pages | 3 |

Journal | Linear Algebra and Its Applications |

Volume | 141 |

Issue number | C |

DOIs | |

State | Published - Nov 1990 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

Lieb, E. H. (1990). On the spectral radius of the product of matrix exponentials.

*Linear Algebra and Its Applications*,*141*(C), 271-273. https://doi.org/10.1016/0024-3795(90)90324-6